1. Technical Field
The present disclosure relates generally to electrical current (“I”) digital-to-analog converters (“IDACs”) particularly for supplying electrical current to light emitting diodes (“LEDs”), most specifically white light emitting diodes (“WLEDs”).
2. Background Art
An IDAC is an important component included in many different types of data converter systems. An IDAC converts binary digital data into an analog electrical current. That is, a particular digital code (number) received by the IDAC specifies that the IDAC is to provide a particular analog current to some other component in a system. Usually, each binary digit (“bit”) in the digital code can be understood as acting on a switch included in the IDAC. Each switch in the IDAC connects between an output of the IDAC and a current source or sink included in the IDAC. Depending upon the value of each bit in the digital code, i.e. 0 or 1, each switch included in the IDAC provides either no current or a specified amount of current to the other system component via the IDAC's output. In this way, operation of all the switches are:                1. controlled respectively by bits in the digital code; and        2. are connected in parallel supply a total output current from the IDAC to the other system component.In conventional integrated circuits (“ICs”), the amount of current supplied by individual IDAC's switches is determined by the IC's physical layout, i.e. the size of individual components included in the IDAC IC. Most frequently, a computer program generates the digital code received by the IDAC that specifies which switches are to be turned on or off. If each of the IDAC's switches supplies the same amount of electrical current to the IDAC's output, it is frequently called a unary IDAC.        
FIG. 1 schematically depicts such a unary IDAC referred to by the general reference character 20. The unary IDAC 20 includes N individual switches 22, SW1 to SWN, each of which connects between an output 24 of the unary IDAC 20 and a current source/sink 26 included in the IDAC. In the schematic illustration of FIG. 1, a second terminal of each of the current sources/sinks 26 connects to circuit ground 28. While FIG. 1 illustrates an unary IDAC that employs several current sinks connected in parallel to circuit ground 28 with a load being implicitly connected between the output 24 and a source of electrical power, as will be apparent to those skilled in the art of analog circuit design a functionally equivalent IDAC may be assembled in which:                1. current sources, as contrasted with current sinks, connect in parallel to the source of electrical power: and        2. the load connects between:                    a. common terminals of all the switches connected respectively in series with the current sources; and            b. circuit ground 28.                        
The unary IDAC 20 receives a digital code K which specifies which of the switches 22 are to either be turned on or turned off. Each switch 22 when turned on supplies or sinks the same amount of electrical current I to or from the output 24. Closing switches 22 causes the unary IDAC 20 depicted in FIG. 1 to draw an electrical current equal to K*I. Because the output current is a linear function of K, the unary IDAC 20 depicted in FIG. 1 is frequently called a linear IDAC.
One specific use for IDACs is controlling electrical current flowing through LEDs used for backlight illumination of displays, e.g. liquid crystal displays (“LCD”). Presently, virtually all consumer devices particular portable devices such as cell phones, tablets, laptops, etc. include a LCD that a user employs in interacting with the device. Presently, display engineers expend more and more effort to make the image appearing on a LCD comfortable to human visual perception in ambient lighting environments that are constantly changing, e.g. moving from inside a building into bright sunlight. Furthermore, devices containing a backlit LCD display may include an ambient light sensor so the device may automatically adapt to changes in ambient lighting without requiring user interaction.
Changes in display brightness that differ from those to which humans are accustomed is at least uncomfortable and may be even stressful to a human viewing an LCD display. Making a backlighting change comfortable to the human eye requires a non-linear current change that increases more rapidly as backlighting becomes brighter. Specifically, accommodating backlighting to human visual perception requires that LCD display brightness conform to the following two (2) basic rules.                1. Changing display brightness should be non-linear in accordance with an exponential, cubic or square law during a time interval.        2. At every instant in time, the relative change in display brightness during the prior instant in time should not exceed one-half of one percent (0.5%).Implementing a backlight illumination function that conforms with two (2) preceding rules is difficult. Implementing such a backlight illumination function requires both digital and analog circuit design skills. Stated more precisely, there presently exists a technological problem in digitally generating a LCD brightness electrical current that changes in accordance with an exponential/cubic/square profile which, at any instant in time, does not change more than one-half of one percent (0.5%).        
FIG. 2 illustrates one technique for generating a staircase non-linear electrical current 32 approximation to an exponential current using an IDAC. The specific technique illustrated in FIG. 2 uses a constant time interval T0 between each change in electrical current, usually a clock signal, and binary weighted current changes (I1<I2<I3<I4<I5<etc.). While in theory one might configure this type of IDAC to exhibit performance in accordance with the two (2) preceding basic rules, present semiconductor fabrication technology cannot provide an accurate non-linear current over a range that extends from very small currents, e.g. nano-amperes (nA), to much larger currents, e.g. one-hundred micro-amperes (100 μA).